圆心与弦的几何关系探究
2017-03-08 04:54
本范例演示了圆的基本性质,重点探究圆心与弦之间的几何关系。通过构造圆、弦以及圆心到弦的垂线段,直观展示了半径、弦长以及圆心到弦的距离之间的内在联系。该交互式模型适合用于中学数学中圆的定理学习与复习。
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.326.0" id="e97f47de-de4f-4065-b5a1-233ee8dd1ec7" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1920" height="1040" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.0" orientation="1" />
</panes>
<views>
<view id="4" toolbar="0 || 2020 , 2021 , 2022 , 66 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="false" location="1,1" size="200" window="0,0,400,400" />
<view id="1" visible="true" inframe="false" stylebar="true" location="1" size="1904" window="0,0,400,400" />
<view id="2" visible="false" inframe="false" stylebar="false" location="3" size="200" window="0,0,200,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 1009 || 66 68 || 6" visible="false" inframe="false" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="16" visible="false" inframe="false" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="64" toolbar="0" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="4097" visible="false" inframe="true" stylebar="true" location="1" size="150" window="710,270,500,500" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="512" toolbar="0 | 1 501 5 19 , 67 | 2 15 45 18 , 7 37 | 514 3 9 , 13 44 , 47 | 16 | 551 550 11 , 20 22 21 23 , 55 56 57 , 12 | 69 | 510 511 , 512 513 | 533 531 , 534 532 , 522 523 , 537 536 , 535 | 521 520 | 36 , 38 49 560 | 571 30 29 570 31 33 | 17 | 540 40 41 42 , 27 28 35 , 6 , 502" visible="false" inframe="false" stylebar="false" location="1" size="300" window="50,50,500,500" />
</views>
<toolbar show="true" items="0 39 73 62 | 1 501 67 , 5 19 , 72 75 76 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49 50 , 71 14 68 | 30 29 54 32 31 33 | 25 17 26 60 52 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="true" cmd="true" top="algebra" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="20"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="1904" height="825"/>
<coordSystem xZero="81.37679545454556" yZero="329.995625" scale="51.366477272727295" yscale="51.36647727272728"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="1" rightAngleStyle="1" checkboxSize="13" gridType="0"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="64" g="64" b="64"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="10"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="1"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="point" label="O">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-12" y="-4"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<isShape val="false"/>
<coords x="5.7357097505668895" y="1.1679918146120216" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="cc">
<show object="false" label="true"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<isShape val="false"/>
<coords x="7.805320502184614" y="-1.214147447596925" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Circle">
<input a0="O" a1="cc"/>
<output a0="c"/>
</command>
<element type="conic" label="c">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="24.304695093979706" A3="0.0" A4="-5.7357097505668895" A5="-1.1679918146120216"/>
<eqnStyle style="specific"/>
</element>
<command name="Point">
<input a0="c"/>
<output a0="A"/>
</command>
<element type="point" label="A">
<show object="true" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-28" y="16"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<isShape val="false"/>
<coords x="8.450793735318557" y="-0.4401733148178113" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="c"/>
<output a0="B"/>
</command>
<element type="point" label="B">
<show object="true" label="true"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="6" y="14"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<isShape val="false"/>
<coords x="2.9910138069774113" y="-0.3890953072320098" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="A" a1="B"/>
<output a0="a"/>
</command>
<element type="segment" label="a">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="-0.0510780075858015" y="-5.4597799283411454" z="-1.9715997227150295"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="point" label="C">
<show object="false" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<isShape val="false"/>
<coords x="9.823979204690001" y="3.9908445329351245" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="a"/>
<output a0="D"/>
</command>
<element type="point" label="D">
<show object="true" label="true" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<isShape val="false"/>
<coords x="5.152213883977145" y="-0.40931403314702436" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Distance">
<input a0="A" a1="D"/>
<output a0="距离AD"/>
</command>
<element type="numeric" label="距离AD">
<value val="3.2987241974649484"/>
<objColor r="255" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="文本AD" exp="Name[A] + (Name[D]) + " = " + 距离AD" />
<element type="text" label="文本AD">
<show object="true" label="false" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<absoluteScreenLocation x="92" y="190"/>
</element>
<command name="Distance">
<input a0="D" a1="B"/>
<output a0="距离DB"/>
</command>
<element type="numeric" label="距离DB">
<value val="2.1612946512915086"/>
<objColor r="255" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="文本DB" exp="Name[D] + (Name[B]) + " = " + 距离DB" />
<element type="text" label="文本DB">
<show object="true" label="false" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<absoluteScreenLocation x="94" y="149"/>
</element>
<command name="Segment">
<input a0="O" a1="D"/>
<output a0="f"/>
</command>
<element type="segment" label="f">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="1.577305847759046" y="-0.5834958665897441" z="-8.365450134580964"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Angle">
<input a0="A" a1="D" a2="O"/>
<output a0="α"/>
</command>
<element type="angle" label="α">
<angleStyle val="1"/>
<value val="1.225831293832362"/>
<show object="true" label="true" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelOffset x="28" y="-17"/>
<labelMode val="2"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<arcSize val="30"/>
</element>
</construction>
</geogebra>